Robust Design in Turbomachinery Applications

A strategy for robust design optimization (RDO) is proposed, i.e., optimization under uncertainties reducing the variability of the system output with respect to the input uncertainties. This strategy relies on the non-intrusive probabilistic collocation method for the uncertainty propagation and a surrogate-assisted optimization strategy. In order to allow for RDO within reasonable turnaround times, a mixed Design of Experiments (DoE) is built, which comprises design variables and uncertainties as individual dimensions. This reduces the cost by one order of magnitude compared to an approach where each point in the DoE is run with a UQ simulation. The robust design optimization problem is formulated as a simultaneous maximization of the mean efficiency and minimization of standard deviations of efficiency and of other global output quantities at the example of the Rotor 37. Three designs on the chosen four-dimensional Pareto front are compared with the deterministic design. The reconstruction of PDFs of global output quantities visualizes their reduced standard deviation. Scaled sensitivity derivatives allow in a direct way to identify the uncertainties, which are responsible for an increase or decrease in sensitivity of output quantities, and they prove to be a very useful tool for the understanding of system dependencies. Full performance curves are run for the selected designs, and the optimal robust designs are discussed. The computational overhead of the presented robust design optimization varies between 1.4 and 1.9 times the computational cost of a deterministic optimization.